Elastic Shell Research Articles

Dramatic droplet deformation through interfacial particles jamming

Droplets of one fluid in a second, immiscible fluid are typically spherical in shape due to the interfacial tension between the two fluids. Shear forces can lead to droplet deformation when they are subjected to flow, and these effects can be further modified when the droplet is stabilized by a surfactant due to a flow-induced gradients in the surfactant concentration. An alternative method of stabilizing droplets is through the use of colloidal particles, whose stabilization behavior is intrinsically different from molecular surfactants. Under the same flow condition, a gradient of particle concentration can result in the jamming of particles in regions with a high packing density, making the interface solid-like, albeit only under compression and not tension. However, how this asymmetry in the surfactant properties alters the droplet shape under shear is unknown. Here, we show that shear of particle-stabilized droplets can lead to a remarkable array of shape deformations as the droplets flow through a constrained microchannel. The shear-induced migration of particles on the surface results in the formation of an elastic shell at the back of the droplet, which can wrinkle and invaginate, ultimately leading to a unique core-shell structure. The shapes depend on the Peclet number of the flow, reflecting the balance of shear forces that drive the particles and diffusion that randomizes them. These findings highlight the consequences of the asymmetry in the forces between the particles and provide a unique method to controllably create droplets with a vast array of different shapes.

Nonlinear Isogeometric Analyses of Instabilities in Thin Elastic Shells Exhibiting Combined Bending and Stretching

Nonlinear Isogeometric Analyses of Instabilities in Thin Elastic Shells Exhibiting Combined Bending and Stretching

Self-locking and stiffening deployable tubular structures

Deployable tubular structures, designed for functional expansion, serve a wide range of applications, from flexible pipes to stiff structural elements. These structures, which transform from compact states, are crucial for creating adaptive solutions across engineering and scientific fields. A significant barrier to advancing their performance is balancing expandability with stiffness. Using compliant materials, these structures achieve more flexible transformations than those possible with rigid mechanisms. However, they typically exhibit reduced stiffness when subjected to external pressures (e.g., tube wall loading). Here, we utilize origami-inspired techniques and internal stiffeners to meet conflicting performance requirements. A self-locking mechanism is proposed, which combines the folding behavior observed in curved-crease origami and elastic shell buckling. This mechanism employs simple shell components, including internal diaphragms that undergo pseudofolding in a confined boundary condition to enable a snap-through transition. We reveal that the deployed tube is self-locked through geometrical interference, creating a braced tubular arrangement. This arrangement gives a direction-dependent structural performance, ranging from elastic response to crushing, thereby offering the potential for programmable structures. We demonstrate that our approach can advance existing deployment mechanisms (e.g., coiled and inflatable systems) and create diverse structural designs (e.g., metamaterials, adaptive structures, cantilevers, and lightweight panels).Weanticipate our design to be a starting point to drive technological advancement in real-world deployable tubular structures.

Convexity conditions for fiber-reinforced elastic shells

Convexity conditions of the Legendre–Hadamard and quasiconvexity type are derived in the context of a theory for fiber-reinforced shells based on Cosserat elasticity. These furnish two-dimensional shell-theoretic versions of their three-dimensional counterparts.

Mathematical modelling of stability problems for thin transversally graded cylindrical shells

The objects of consideration are thin linearly elastic Kirchhoff–Love-type open circular cylindrical shells having a functionally graded macrostructure and a tolerance-periodic microstructure in circumferential direction. The first aim of this contribution is to formulate and discuss a new mathematical averaged non-asymptotic model for the analysis of selected stability problems for such shells. As a tool of modelling we shall apply the tolerance averaging technique. The second aim is to derive and discuss a new mathematical averaged asymptotic model. This model will be formulated using the consistent asymptotic modelling procedure. The starting equations are the well-known governing equations of linear Kirchhoff–Love second-order theory of thin elastic cylindrical shells. For the functionally graded shells under consideration, the starting equations have highly oscillating, non-continuous and tolerance-periodic coefficients in circumferential direction, whereas equations of the proposed models have continuous and slowly-varying coefficients. Moreover, some of coefficients of the tolerance model equations depend on a microstructure size. It will be shown that in the framework of the tolerance model not only the fundamental cell-independent, but also the new additional cell-dependent critical forces can be derived and analysed.

Numerical analysis of ultrasound-mediated microbubble interactions in vascular systems: Effects on shear stress and vessel mechanics

The present study concerns the numerical modeling of microbubble oscillation within an elastic microvessel, aiming to enhance the safety and efficacy of ultrasound-mediated drug delivery and diagnostic imaging. The success of such applications depends on a thorough understanding of microbubble–vessel interactions. Despite some progress, the critical impact of the stabilizing shell around gas core has remained underexplored. To address this, we developed a novel numerical approach that models the stabilizing shell. Additionally, there is novelty in modeling consequent vascular deformation in response to complicated spatiotemporal microbubble oscillations. The novel approach was implemented for shear stress evaluation as a critical factor in vascular permeability. Finally, our unique approach offered novel insights into microbubble–vessel interactions under diverse acoustic conditions. Results indicated substantial impact of shell properties and acoustic parameters on induced shear stress. With a fourfold increase in acoustic pressure amplitude, 15.6-fold and sixfold increases were observed in maximum shear stress at 1 and 3 MHz, respectively. Also, the peak shear stress could reach up to 15.6 kPa for a shell elasticity of 0.2 N/m at 2.5 MHz. Furthermore, decreasing microvessel/bubble size ratio from 3 to 1.5 increased maximum shear stress from 5.1 to 24.3 kPa. These findings are crucial for optimizing ultrasound parameters in clinical applications, potentially improving treatment outcomes while minimizing risk of vessel damage. However, while our model demonstrated high fidelity in reproducing experimental observations, it is limited by assumptions of vessel geometry and homogeneity of vessel properties. Future work can improve our findings through in vitro experimental measurements.

Uncertainty quantification for locally resonant coated plates and shells

The effect of uncertainty in design parameters on the acoustic performance of coated plates and coated shells for maritime applications is presented. The locally resonant coatings are designed using a viscoelastic material with an impedance similar to water and embedded with layers of inclusions. Both voids and hard inclusions, which respectively exhibit monopole and dipole resonance scattering, are considered. Effective medium approximation theory is employed to characterise the layers of inclusions as homogenised layers with effective material and geometric properties. The coating is then modelled as a multilayered equivalent fluid composed of alternating layers of the homogeneous viscoelastic material and the homogenised layers of inclusions. The coating is bonded to a rigid backing plate and the acoustic response is calculated using the transfer matrix method. The coating is also externally applied to an elastic cylindrical shell. The acoustic response is calculated by expressing the shell displacements and acoustic pressures in the coating and exterior domain in terms of Fourier series expansions, and applying continuity equations at each interface between the shell surface, coating layers and the surrounding water. Efficient stochastic models based on the non-intrusive polynomial chaos expansion (PCE) method are developed by transforming the analytical models for the coated plates and shells into computationally efficient surrogate models using point collocation. Uncertainty in dominant design parameters associated with the geometry of the inclusions and material properties of the coating is examined. The influence of the design parameters for inclusions tuned to different resonance frequencies and for multiple layers of inclusions is also reported. Strong acoustic performance of coating designs occurs in a broad frequency range around local resonance of the inclusions. For all coating models, uncertainty in parameters which predominantly influence the local resonance of the inclusions were observed to yield the greatest variation in the acoustic responses of the coated plates and shells.

On the numerical corroboration of an obstacle problem for linearly elastic flexural shells.

In this article, we study the numerical corroboration of a variational model governed by a fourth-order elliptic operator that describes the deformation of a linearly elastic flexural shell subjected not to cross a prescribed flat obstacle. The problem under consideration is modelled by means of a set of variational inequalities posed over a non-empty, closed and convex subset of a suitable Sobolev space and is known to admit a unique solution. Qualitative and quantitative numerical experiments corroborating the validity of the model and its asymptotic similarity with Koiter's model are also presented.This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.

Deflagration inside an elastic spherical shell: Fluid-structure interaction effects

We examine the problem of deflagration of a flammable gaseous mixture contained within an elastic spherical shell and ignited at its centre. We predict analytically the pressure wave radiated by an expanding spherical deflagration front and we study its interaction with the elastic shell prior to failure. We predict the waves reflected at the inner wall of the shell and radiated in the space outside the shell, which we assume initially filled with air at atmospheric pressure, and we calculate the magnitude of these waves as a function of density, thickness and elastic modulus of the shell. The findings of this model are used to critically assess laboratory setups used in controlled deflagration experiments, in which a flammable mixture is initially contained by a soft shell. The interpretation of data from these tests currently assumes that the gaseous mixture is effectively unconfined during the deflagration, due to the low mass, low stiffness and early failure of the containing shell. We show that this assumption is not adequate and it leads to errors in the interpretation of the measurements; the proposed model is used to quantify these errors.

From elastic shallow shells to beams with elastic hinges by Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document}-convergence

In this paper, we study the Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document}-limit of a properly rescaled family of energies, defined on a narrow strip, as the width of the strip tends to zero. The limit energy is one-dimensional and is able to capture (and penalize) concentrations of the midline curvature. At the best of our knowledge, it is the first paper in the Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document}-convergence field for dimension reduction that predicts elastic hinges. In particular, starting from a purely elastic shell model with “smooth” solutions, we obtain a beam model where the derivatives of the displacement and/or of the rotation fields may have jump discontinuities. Mechanically speaking, elastic hinges can occur in the beam.

Acoustic radiation force on a cylindrical composite particle with an elastic thin shell and an internal eccentric liquid column in a plane ultrasonic wave field

Abstract A model with three-layer structure is introduced to explore the acoustic radiation force (ARF) on composite particles with an elastic thin shell. Combing acoustic scattering of cylinder and the thin-shell theorem, the ARF expression was derived, and the longitudinal and transverse components of the force and axial torque for an eccentric liquid-filled composite particle was obtained. It was found that many factors, such as medium properties, acoustic parameters, eccentricity, and radius ratio of the inner liquid column, affect the acoustic scattering field of the particle, which in turn changes the forces and torque. The acoustic response varies with the particle structures, so the resonance peaks of the force function and torque shift with the eccentricity and radii ratio of particle. The acoustic response of the particle is enhanced and exhibits higher force values due to the presence of the elastic thin shell and the coupling effect with the eccentricity of the internal liquid column. The decrease of the inner liquid density may suppress the high-order resonance peaks, and internal fluid column has less effects on the change in force on composite particle at ka > 3, while limited differences exist at ka < 3. The axial torque on particles due to geometric asymmetry is closely related to ka and the eccentricity. The distribution of positive and negative force and torque along the axis ka exhibits that composite particle can be manipulated or separated by ultrasound. Our theoretical analysis can provide support for the acoustic manipulation, sorting, and targeting of inhomogeneous particles.

Flexible arch-shaped triboelectric sensor based on 3D printing for badminton movement monitoring and intelligent recognition of technical movements

Efficient monitoring and recognition of movement are crucial in enhancing athletic performance. Traditional methods have limitations in terms of high site requirements and power consumption, making them unsuitable for long-term tracking and monitoring. A potential solution to low-power monitoring of body area networks is triboelectric sensors. However, the current analysis method for badminton triboelectric sensing data is relatively simple, while flexible, triboelectric sensors based on 3D printing face issues such as discomfort when joints are bent or twisted in a large range. In light of this, a flexible arch-shaped triboelectric sensor based on 3D printing (FA-Sensor) is proposed. By combining neural network algorithms with the signal acquisition module and the master computer, an intelligent multi-sensor node system for badminton monitoring is established. The FA-Sensor exhibits high sensitivity to bending and twisting motions due to its elastic TPE shell and arched shape design. It minimizes interference with human motion during bending (10°–150°) or twisting (20°–100°) over a wide range. The peak output voltage of the FA-Sensor demonstrates a clear functional relationship with the bending angle, exhibiting piecewise sensitivities of 7.98 and 29.28 mV/°, respectively. For seven different parts of the human body, it can be quickly customized to different sizes, with stable and repeatable response outputs. In application, the badminton sports monitoring system enables real-time feedback and recognition of four typical technical movements, achieving a recognition accuracy rate of 97.2%. The system enables athletes to analyze and enhance badminton technology while also exhibiting promising potential for application in other intelligent sports domains.

Microscale geometrical modulation of PIEZO1 mediated mechanosensing through cytoskeletal redistribution

The microgeometry of the cellular microenvironment profoundly impacts cellular behaviors, yet the link between it and the ubiquitously expressed mechanosensitive ion channel PIEZO1 remains unclear. Herein, we describe a fluorescent micropipette aspiration assay that allows for simultaneous visualization of intracellular calcium dynamics and cytoskeletal architecture in real-time, under varied micropipette geometries. By integrating elastic shell finite element analysis with fluorescent lifetime imaging microscopy and employing PIEZO1-specific transgenic red blood cells and HEK cell lines, we demonstrate a direct correlation between the microscale geometry of aspiration and PIEZO1-mediated calcium signaling. We reveal that increased micropipette tip angles and physical constrictions lead to a significant reorganization of F-actin, accumulation at the aspirated cell neck, and subsequently amplify the tension stress at the dome of the cell to induce more PIEZO1’s activity. Disruption of the F-actin network or inhibition of its mobility leads to a notable decline in PIEZO1 mediated calcium influx, underscoring its critical role in cellular mechanosensing amidst geometrical constraints.

Numerical simulation of nanoneedle-cell membrane collision: minimum magnetic force and initial kinetic energy for penetration

Aims and objectives: This research aims to develop a kinetic model that accurately captures the dynamics of nanoparticle impact and penetration into cell membranes, specifically in magnetically-driven drug delivery. The primary objective is to determine the minimum initial kinetic energy and constant external magnetic force necessary for successful penetration of the cell membrane. Model Development: Built upon our previous research on quasi-static nanoneedle penetration, the current model development is based on continuum mechanics. The modeling approach incorporates a finite element method and explicit dynamic solver to accurately represent the rapid dynamics involved in the phenomenon. Within the model, the cell is modeled as an isotropic elastic shell with a hemiellipsoidal geometry and a thickness of 200 nm, reflecting the properties of the lipid membrane and actin cortex. The surrounding cytoplasm is treated as a fluid-like Eulerian body. Scenarios and Results: This study explores three distinct scenarios to investigate the penetration of nanoneedles into cell membranes. Firstly, we examine two scenarios in which the particles are solely subjected to either a constant external force or an initial velocity. Secondly, we explore a scenario that considers the combined effects of both parameters simultaneously. In each scenario, we analyze the critical values required to induce membrane puncture and present comprehensive diagrams illustrating the results. Findings and significance: The findings of this research provide valuable insights into the mechanics of nanoneedle penetration into cell membranes and offer guidelines for optimizing magnetically-driven drug delivery systems, supporting the design of efficient and targeted drug delivery strategies.

Efficient large-deformation shell elements for the simulation of electromechanical coupling effects in incompressible dielectric elastomers

So-called electro-active polymers are not only capable of undergoing very large deformations, but they also exhibit different electromechanical coupling effects due to their dielectric or electrostrictive characteristics. In the present paper the sub-class of dielectric elastomers is studied; in particular, we focus on thin dielectric elastomer shells, which undergo large deformations under an applied electric field. We develop a framework for the modeling and subsequent efficient simulation of thin structures made from incompressible dielectric elastomers. A thermodynamically consistent phenomenological continuum model based on the free energy density is adapted imposing the kinematic assumptions of Kirchhoff-Love shells in combination with including the thickness deformation and the electric field as independent unknown fields. To make the formulation accessible to finite element simulations, existing non-linear elastic shell mixed finite elements are extended to the present hyperelastic electromechanically coupled formulation for dielectric elastomer shells. Computational results of the shell theory are compared to three-dimensional results validating the proposed modeling and numerical simulation methodology, and showing high accuracy already for coarse finite element discretizations of the shell.

Acoustic Radiation Force on an Arbitrarily Placed Elastic Spherical Shell near an Impedance Boundary for Bessel Waves

Acoustic Radiation Force on an Arbitrarily Placed Elastic Spherical Shell near an Impedance Boundary for Bessel Waves

Are monodisperse phospholipid-coated microbubbles “mono-acoustic?”

Phospholipid-coated microbubbles with a uniform acoustic response are a promising avenue for functional ultrasound sensing. A uniform acoustic response requires both a monodisperse size distribution and uniform viscoelastic shell properties. Monodisperse microbubbles can be produced in a microfluidic flow focusing device. Here, we investigate whether such monodisperse microbubbles have uniform viscoelastic shell properties and thereby a uniform “mono-acoustic” response. To this end, we visualized phase separation of the DSPC and DPPE-PEG5000 lipid shell components and measured the resonance curves of nearly 2000 single and freely floating microbubbles using a high-frequency acoustic scattering technique. The results demonstrate inhomogeneous phase-separated shell microdomains across the monodisperse bubble population, which may explain the measured inhomogeneous viscoelastic shell properties. The shell viscosity varied over an order of magnitude and the resonance frequency by a factor of two indicating both a variation in shell elasticity and in initial surface tension despite the relatively narrow size distribution.

Identification of excessive contact pressures under hand orthosis based on finite element analysis.

Implicit magnitudes and distribution of excessive contact pressures under hand orthoses hinder clinicians from precisely adjusting them to relieve the pressures. To address this, contact pressure under a hand orthosis were analysed using finite element method. This paper proposed a method to numerically predict the relatively high magnitudes and critical distribution of contact pressures under hand orthosis through finite element analysis, to identify excessive contact pressure locations. The finite element model was established consisting of the hand, orthosis and bones. The hand and bones were assumed to be homogeneous and elastic bodies, and the orthosis was considered as an isotropic and elastic shell. Two predictions were conducted by assigning either low (fat) or high (skin) material stiffness to the hand model to attain the range of pressure magnitudes. An experiment was conducted to measure contact pressures at the predicted pressure locations. Identical pressure distributions were obtained from both predictions with relatively high pressure values disseminated at 12 anatomical locations. The highest magnitude was found at the thumb metacarpophalangeal joint with the maximum pressure range from 13 to 78 KPa. The measured values were within the predicted range of pressure magnitudes. Moreover, 6 excessive contact pressure locations were identified. The proposed method was verified by the measurement results. It renders understanding of interface conditions underneath the orthosis to inform clinicians regarding orthosis design and adjustment. It could also guide the development of 3D printed or sensorised orthosis by indicating optimal locations for perforations or pressure sensors.

Patterning of multicomponent elastic shells by gaussian curvature.

Recent findings suggest that shell protein distribution and the morphology of bacterial microcompartments regulate the chemical fluxes facilitating reactions which dictate their biological function. We explore how the morphology and component patterning are coupled through the competition of mean and gaussian bending energies in multicomponent elastic shells that form three-component irregular polyhedra. We observe two softer components with lower bending rigidities allocated on the edges and vertices while the harder component occupies the faces. When subjected to a nonzero interfacial line tension, the two softer components further separate and pattern into subdomains that are mediated by the gaussian curvature. We find that this degree of fractionation is maximized when there is a weaker line tension and when the ratio of bending rigidities between the two softer domains ≈2. Our results reveal a patterning mechanism in multicomponent shells that can capture the observed morphologies of bacterial microcompartments, and moreover, can be realized in synthetic vesicles.

Chromatin phase separation and nuclear shape fluctuations are correlated in a polymer model of the nucleus

ABSTRACT Abnormal cell nuclear shapes are hallmarks of diseases, including progeria, muscular dystrophy, and many cancers. Experiments have shown that disruption of heterochromatin and increases in euchromatin lead to nuclear deformations, such as blebs and ruptures. However, the physical mechanisms through which chromatin governs nuclear shape are poorly understood. To investigate how heterochromatin and euchromatin might govern nuclear morphology, we studied chromatin microphase separation in a composite coarse-grained polymer and elastic shell simulation model. By varying chromatin density, heterochromatin composition, and heterochromatin-lamina interactions, we show how the chromatin phase organization may perturb nuclear shape. Increasing chromatin density stabilizes the lamina against large fluctuations. However, increasing heterochromatin levels or heterochromatin-lamina interactions enhances nuclear shape fluctuations by a “wetting”-like interaction. In contrast, fluctuations are insensitive to heterochromatin’s internal structure. Our simulations suggest that peripheral heterochromatin accumulation could perturb nuclear morphology, while nuclear shape stabilization likely occurs through mechanisms other than chromatin microphase organization.